A plan to lift the city’s 4 percent sales tax on home heating fuels got snared in a political dispute yesterday that left homeowners out in the cold.

Two bills were separately enacted by the Assembly and state Senate – either of which would provide relief to property owners who’ve fumed as their fuel bills doubled, and sometimes tripled, this frigid winter.

But the bills won’t do anyone any good until the two bodies can agree.

The bill sponsored by state Sen. Roy Goodman (R-Manhattan) would permit the city to yank the tax on heating oil and natural gas for 60 days, but just this year.

The bill sponsored by Assembly Speaker Sheldon Silver (D-Manhattan) would give the mayor and the City Council the right to lift the tax on all heating fuels at any time, even permanently.

Mayoral aides said Silver’s bill could cost the city as much as $175 million, way beyond what the city envisioned.

The administration first proposed removing the heating-oil tax for January and February, saving taxpayers about $8 million. Natural gas users clamored for the same deal and the administration agreed, upping the price for the package to about $30 million.

“We’re not necessarily certain this tax should go away,” Michelle Goldstein, a city budget official, testified before the City Council.

“This is just an emergency measure to help consumers out for this winter.”

That left Councilman Gifford Miller (D-Manhattan) exasperated.

“The Assembly bill would allow the city to make the decision,” Miller declared. “The Senate bill makes the decision for the city.”

In the past, the mayor has criticized Albany for dictating tax policies that the city had to follow.

There will be no tax relief for heating fuel unless the Senate and Assembly can come to terms on one bill.

A Con Ed official estimated that the average homeowner using natural gas would save $12.50 a month if the tax is repealed.

Councilwoman Madeline Provenzano (D-Bronx) called on all sides to stop “fiddling around.”

“Before anything is done, we’re probably into March,” she said. “What good is this going to do any of us because we’ve passed December, January, February, which are the big bill months?”